If f(x) = 5x – 6, what is the equation for f–1(x)?

Cory's percent error for his trip time prediction was 13.5% after rounding to the nearest tenth of a percent.

To calculate Cory's percent error for predicting his travel time to Baltimore from Washington D.C., we can use the formula for percent error:

Percent Error =[tex]|(Actual Value - Predicted Value) / Actual Value| \times 100%[/tex]

In this case, Cory's predicted time (Predicted Value) is 64 minutes, and the actual time taken (Actual Value) is 74 minutes. We can plug these values into the formula:

Percent Error = [tex]|(74 - 64) / 74| \times 100%[/tex]
Percent Error = [tex]|10 / 74| \times 100%[/tex]
Percent Error =[tex]0.1351 \times 100%[/tex]

Calculating further:

Percent Error = 13.51%

When rounded to the nearest tenth, Cory's percent error is 13.5%.

Twenty-five squares with a side length of 6 inches are required to cover a square with a side length of 30 inches.

To find out how many squares with sides that are 6 inches long are needed to cover a square with a length of 30 inches, you first need to find the area of each square.

The area of a square is found by multiplying the length of one side by itself.

So, the area of the smaller square is 6 * 6 = 36 square inches, and

the area of the larger square is 30 * 30 = 900 square inches.

Then, you divide the area of the larger square by the area of the smaller square:

          900/36 = 25.

Therefore, 25 squares with sides of 6 inches are needed to cover a square with a side length of 30 inches.

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x = hamburgers

2x = cheeseburgers

x +2x = 345

3x = 345

x = 345/3 = 115

115 hamburgers were sold

The solution to this system is (x, y) = (8, -22).

The y-values get closer together by 2 units for each 2-unit increase in x. The difference at x=2 is 6, so we expect the difference in y-values to be zero when we increase x by 6 (from 2 to 8).

You can extend each table after the same pattern.

In table 1, x-values increase by 2 and y-values decrease by 8.

In table 2, x-values increase by 2 and y-values decrease by 6.

The attachment shows the tables extended to x=10. We note that the y-values are the same (-22) for x=8 (as we predicted above). That means the solution is ...

... (x, y) = (8, -22)

Answer:

(8,-22)

Step-by-step explanation:

Table 1)

To form equation we will use two point slope form

[tex](x_1,y_1)=(-4,26)\\(x_2,y_2)=(-2,18)[/tex]

Formula :[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Substitute the values :

[tex]y-26=\frac{18-26}{-2+4}(x+4)[/tex]

[tex]y-26=-4(x+4)[/tex]

[tex]y-26=-4x-16[/tex]

[tex]y=-4x-16+26[/tex]

[tex]y=-4x+10[/tex] ---1

Table 2)

To form equation we will use two point slope form

[tex](x_1,y_1)=(-4,14)\\(x_2,y_2)=(-2,8)[/tex]

Formula :[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Substitute the values :

[tex]y-14=\frac{8-14}{-2+4}(x+4)[/tex]

[tex]y-14=-3(x+4)[/tex]

[tex]y-14=-3x-12[/tex]

[tex]y=-3x+2[/tex] ---2

Now we are supposed to solve 1 and 2

Substitute the value of y from 1 in 2

[tex]-4x+10=-3x+2[/tex]

[tex]8=x[/tex]

Substitute the value of x in 2

[tex]y=-3(8)+2[/tex]

[tex]y=-22[/tex]

Hence the solution to this system is (8,-22)

The given differential equation (3x + 6y) dx + (6x − 8y3) dy = 0 is exact because its mixed partial derivatives are equal. To solve it, first integrate M with respect to x to get a function involving an unknown function of y, then compare it with N to determine the unknown function.

To determine if the given differential equation is exact, we need to check if the partial derivative of M with respect to y is the same as the partial derivative of N with respect to x. In this given differential equation (3x + 6y) dx + (6x − 8y3) dy = 0, M = 3x + 6y and N = 6x - 8y3. First, compute the partial derivative of M with respect to y (∂M/∂y) which is 6, then the partial derivative of N with respect to x (∂N/∂x), which is 6 as well. Since ∂M/∂y=∂N/∂x, the given differential equation is exact.

To solve this exact differential equation, we integrate M dx, i.e., ∫M dx, to get ψ(x,y) =1.5x^2+6xy+h(y), where h(y) is an arbitrary function of y. Next, differentiate ψ(x,y) with respect to y, then compare the result with N: ψy=6x+dh/dy=6x-8y³. Solving for dh/dy gives dh/dy=-8y³, so integrating this gives h(y)=-2y⁴+C, where C is a constant. Therefore, the solution to the differential equation is ψ(x,y)=1.5x²+6xy-2y⁴=C.

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The percentage increase of the notebook is 14.3%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the price of a notebook was $3.50 yesterday. Today, the price rose to $4.00

The percent increase will be calculated as,

P = [ (4.00 - 3.50) / 3.50 ] x 100

P = [ 0.50 / 3.50 ] x 100

P = 0.1428 x  100

P = 14.28% or 14.3%

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total length of the line is:

 J = -10

K = 8

for a total of 18 units long

 midpoint would be 18/2 =9

-10+9 = -1

 so need the point that is located at negative 1, which is point N

 so N is the midpoint

Answer:

200

Step-by-step explanation:

So say the dominoes' short side is x. Then the long side is 2x, so altogether there is 6x. So 6x=60, so x=10. So the area is 10*(10*2), which is 10*20 which is 200.

Answer:

66,000 units

Step-by-step explanation:

Break-Even Sales (units) = Fixed Costs ÷ Unit Contribution Margin = $561,000 ÷ ($8 + $0.50) = 66,000 units

The break-even point in units after the decrease in variable costs is 66,000 units.

Given that the fixed costs are $561,000 and the original unit contribution margin is $8.00, we first calculate the original break-even point:

[tex]\[ \text{Original Break-even point in units} = \frac{561,000}{8} \][/tex]

[tex]\[ \text{Original Break-even point in units} = 70,125 \text{ units} \][/tex]

Now, since variable costs are decreased by $0.50 a unit, the new unit contribution margin becomes:

[tex]\[ \text{New Unit Contribution Margin} = 8 + 0.50 \][/tex]

[tex]\[ \text{New Unit Contribution Margin} = 8.50 \][/tex]

Using the new unit contribution margin, we calculate the new break-even point:

[tex]\[ \text{New Break-even point in units} = \frac{561,000}{8.50} \][/tex]

[tex]\[ \text{New Break-even point in units} = 66,000 \text{ units} \][/tex]

Therefore, the new break-even point in units, after the decrease in variable costs, is 66,000 units.

All of the expressions are equivalent except (b) -4 + y.

All the expressions involve adding -4 and - y in various orders, resulting in equivalent expressions due to the commutative property of addition.

However, the expression -4 + y  is different because it combines the positive y term with the negative 4, resulting in - 4 + y.

The other expressions either have y added to -4 ( -4 - y) or have -4 added to y (-y - 4, -y + (-4)).

While addition is commutative, changing the order of the terms can affect the overall expression when dealing with negative terms.

So, while mathematically equivalent, the form of -4 + y stands out due to its structure.

Complete Question:

All of the following expressions are equivalent except _____.

(a) -4 - y

(b) -4 + y

(c) -y - 4

(d) -y + (-4 )

Answer:

The Meaning of term Variable is that Quantity Represented by small or Capital Alphabets of English whose value is not fixed.It can vary on different Situations.For example , Human diet can be called Variable.

In morning , you ate total of 0.25 Kg, in Afternoon you ate =0.50 Kg in total, and in the evening you ate total of 1 Kg.

So, if x is a variable of my Diet taken from Morning to evening, it has taken three distinct values, which are, x= 0.25, 0.50,1.

Here, x is a Variable, and 0.25,0.50 and 1 are Constant.

After solving the equations, it is found that there are 32 pennies in the jar.

To solve the problem of determining the number of pennies in the jar, first we establish two variables: let's denote P for the number of pennies and N for the number of nickels.

According to the problem, there are 56 coins in total, which gives us the equation P + N = 56. Also, we know that the total value of the coins is $1.52, and because each penny is worth 1 cent and each nickel is worth 5 cents, we have another equation, which is P + 5N = 152 (since there are 100 cents in a dollar).

Now we have a system of two equations to work with:

P + N = 56

P + 5N = 152

To find P, we can subtract the first equation from the second equation to eliminate P and solve for N:
0P + 4N = 96

N = 96 / 4

N = 24

Now that we know there are 24 nickels, we can find the number of pennies by substituting N back into the first equation:

P + 24 = 56

P = 56 - 24

P = 32

Therefore, there are 32 pennies in the jar.

#2 is the correct answer

 5h would be the amount he earned helping his brother

+ 26 is how much he has

 so those 2 amounts need to equal or be greater than 48

The parametric vector equations for the parabola y=x² from the origin to the point (3,9) is x = t and y = t² for the parameter range 0 <= t <= 3.

The required parametric vector equation for the parabola y=x² from the origin to the point (3,9) is given by the equations x = t and y = t². Here, t is the parameter. At t=3, these equations give us the coordinates x=3 and y=9, which corresponds to the point (3,9). Thus, these equations accurately represent the parabola y=x² from the origin to the point (3,9) for the parameter range 0 <= t <= 3.

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In the parametric form, the path of a point on the parabola y=x² from the origin to point (3,9) is represented by a vector (t, t²) with t ranging from 0 to 3.

To find a vector parametric equation for the parabola y=x² from the origin to the point (3,9), we first need to understand that the parabola y = x² is not a vector in itself.

But, we can describe its trajectory through a parametric form using t as a parameter. For a given t, the parabola is represented by a vector (x(t), y(t)), where x(t) and y(t) are functions of t. For the specific parabola y = x², we can define the functions as x(t) = t and y(t) = t².

This means the vector at time t is given by (t, t²). From the origin (0,0) to the point (3,9), we now have a parameter t ranging from 0 to 3.

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There are 667 positive integers not exceeding 1000 that are not divisible by either 4 or 6.

This is a question about number theory and involves the comprehension of divisibility. To identify the positive integers that are not divisible by either 4 or 6 and not exceeding 1000 is an application of the principle of inclusion and exclusion.

First, we need to figure out how many numbers up to 1000 are divisible by 4, which is 1000/4 = 250. Then, we look at how many numbers are divisible by 6, which is 1000/6 = about 166 (we only consider the whole numbers).

However, some numbers are divisible by both 4 and 6, so we have over-counted and need to correct for this. These would be the numbers divisible by the least common multiple (LCM) of 4 and 6, which is 12. There are 1000/12 = about 83 such numbers.

Thus, according to the principle of inclusion and exclusion, the total number of numbers divisible by 4 or 6 would be 250 + 166 - 83 = 333. The last step is to subtract this from the total number of integers from 1 to 1000, so the answer would be 1000 - 333 = 667.

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Final answer:

The tree in Carlos' backyard is 5 meters high, which is equivalent to 500 centimeters because there are 100 centimeters in a meter. Multiplying 5 meters by 100 gives us the height in centimeters.

Explanation:

To convert the height of the tree in Carlos' backyard from meters to centimeters, we need to know the conversion factor between these two units of measurement. There are 100 centimeters in a meter. Therefore, if the tree is 5 meters high, to find its height in centimeters, we multiply 5 meters by 100.

5 meters × 100 centimeters/meter = 500 centimeters

So, the tree is 500 centimeters tall when converted from meters. This is similar to the example given where Corey measures a distance of 8 meters between two trees and wants to convert that measurement to centimeters. In this concept, we are provided insight into converting with metric units of measurements which is crucial for accurately understanding dimensions in different units.

The value of the solution of expression is, x = 6

We have to give that,

An expression to simplify,

5x - 7 = 3x + 5

Now, Simplify the expression by combining like terms as,

5x - 7 = 3x + 5

Subtract 3x on both sides,

5x - 3x - 7 = 3x + 5 - 3x

2x - 7 = 5

Add 7 on both sides,

2x - 7 + 7 = 5 + 7

2x = 12

Divide 2 into both sides,

x = 12/2

x = 6

Therefore, the solution is, x = 6

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